Fast Ray Tracing Routine for Laterally Inhomogeneous Media

摘要

This document describes the use of continuation or homotopy procedures in an efficient algorithm for the calculation of raypaths from points within a region at depth to receivers on the surface. Polynomials define the interfaces in a two-dimensional piecewise constant velocity medium. Starting with horizontal layering only, the interfaces are gradually deformed until the desired earth model is achieved. At each deformation step the ray equations determined by Fermat's Principle are solved using Newton's method and the ray from the first source position to a receiver vertically above it is found. Next the author employs source continuation, moving the source on a grid within the region of interest. At each source position he finds the rays to all receivers using continuation in receiver location. Knowing the raypaths, it is straightforward to construct a table of traveltimes. These traveltimes alone serve to position reflectors in the subsurface. Two examples of migration and indicate possible applications to forward modeling are given. (Author)